A discussion of a device proposed by Fulkerson and Ford for maximal multi-commodity network flows. A machine-job scheduling model is formulated that avoids the usual in-process inventories and that has fewer equations. The activities are the possible sequence, for each job, of machine steps and interspersed delays which greatly multiply the number of activities. However, a compact network representation of the set of possible activities is developed which permits the generating of just the activity to enter the basis on each iteration without explicitly generating the others. This is accomplished by using one of the efficient procedures that now exist for computing the shortest route through a network.
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